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Understanding the 

Temperature and Humidity 

Environment Inside a PV 

Module 

2013 NREL PVMRW

Michael Kempe

Wednesday, February 27, 2013

NREL/PR-5200-58375
2

Introduction 

• Many degradation processes within a PV 

module are driven by moisture. 

• The concentration of moisture in a module is a 

complex function of the use environment and 

the module construction.

• In accelerated stress testing one must know how 

water affects degradation to determine what 

temperature and humidity conditions to use. 

• Here we show that by choosing humidity 

conditions that more closely match the use 

environment, one can minimize the uncertainty 

associated with moisture induced degradation 

modes.
3

Outline 

• Describe moisture on the backside of a module.

• Look at the hydrolysis of a typical back-sheet 

made of PET as a case study for comparing 85 

0C/85% RH to outdoor exposure. 

• Examine the moisture and temperature 

environment on the front of a module as a worst 

case scenario.

• Show how good choices for RH testing will 

minimize uncertainty.
4

Representative Module Environment

• Use either IWEC or 

TMY-3 data for select 

environments.

• Use the model of 

King et al.* for 

module temperature.

• This produces 

“representative” data 

intended to generally 

duplicate a use 

environment

20

30

40

50

60

70

80

0 1 2 3 4 5

Module Temperature (0C)

Days

Bangkok Thailand Module Temperature

Insulated Back, Glass/Polymer Close Roof, Glass/Glass Open Rack, glass/glass open Rack, Glass/Polymer

*D. L. King, W. E. Boyson, and J. A. Kratochvil, "Photovoltaic array 

performance model," SAND2004-3535, Sandia National 

Laboratories, Albuquerque, NM, 2004.

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5

Relative Humidity Module 

Surface (%)

Days

Bangkok Thailand Ambient Relative Humidity at 

Module Temperature

Insulated Back, Glass/Polymer Close Roof, Glass/Glass Open Rack, glass/glass open Rack, Glass/Polymer
5

Moisture in the Back-EVA Layer

• Assume diffusivity in EVA is much greater 

than in the back-sheet.

• Also assume transient moisture gradient in 

the back-sheet is unimportant.

dCE

dd

=

WVVVB,SSS

CE,SSSlE

CE,EE − CE

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016

0.0018

0.002

0 1 2 3 4 5

Absolute Humidity (g/cm3)

Days

Bangkok Thailand Module Back-EVA Absolute Humidity

Insulated Back,

Glass/Polymer

Close Roof, Glass/Glass

Open Rack, glass/glass

open Rack, Glass/Polymer

Back-Sheet 

 

 Glass

H2O 

Back-EVA

PV Front-EVA

Cell
6

Back-Sheet Exposure

• A PET based back-sheet will be exposed to humidity 

between that outside and inside the module.

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5

Relative Humidity (%)

Days

Bangkok Thailand Back-Sheet Relative Humidity

Insulated Back, Glass/Polymer Inside

Close Roof, Glass/Glass Inside

Open Rack, glass/glass Inside

open Rack, Glass/Polymer Inside

Insulated Back, Glass/Polymer Outside

Close Roof, Glass/Glass Outside

Open Rack, glass/glass Outside

open Rack, Glass/Polymer Outside
7

Pet Hydrolysis Kinetics

lll C

C−x

= A ∙ t ∙ RR2 ∙ e

−E

kk 

Ea=129.4 kJ/mol (1.340 eV), A=2.84·1010 1/day, RH expressed as a percentage.

 

*PET becomes brittle (1/3 initial tensile strength) and “failed” when log(C/C-x)=~0.0024, 

or about 0.55% hydrolysis of ester bonds. 

**Pickett et. al saw the activation energy vary between 125 and 151 kJ/mol with an 

average of 136±13 kJ/mol for four different PET grades. 

O

O O

O

PolyEthylene Terepthalate (PET)

n

H H

+ O O

O O

O H

n-x

HO O

O O

O

x

+

*W. McMahon, H. A. Birdsall, G. R. Johnson, and C. T. Camilli, "Degradation Studies of Polyethylene Terephthalate," Journal of Chemical & Engineering Data, vol. 4, pp. 57-79, 1959. 

**J. E. Pickett and D. J. Coyle, "Hydrolysis Kinetics of Condensation Polymers Under Humidity Aging Conditions," Submitted to the Journal of Polymer Degradation and Stability, 2013.
8

PET Hydrolysis Results

lll C

C−x

= A ∙ t ∙ RR2 ∙ e

−E

kk 

Open 

Rack

Insulated 

Back

Open 

Rack

Insulated 

Back

Open 

Rack

Insulated 

Back

Open 

Rack

Insulated 

Back

Denver, Colorado 13,000 4,900 6,500 2,400 5.3 8.7 45 49

Munich, Germany 11,000 4,400 5,100 2,100 6.0 9.2 47 50

Albuquerque, New Mexico 9,000 3,200 4,400 1,500 6.4 11 48 52

Riyadh, Saudi Arabia 8,200 3,000 4,000 1,500 6.7 11 48 52

Phoenix, Arizona 3,400 1,300 1,700 630 10 17 54 58

Miami, Florida 1,100 510 530 250 19 27 62 65

Bangkok, Thailand 700 310 320 150 24 34 66 69

Relative Humidity 

at 850C so that 

1000 h equals 25 

years exposure 

(%)

Temperature at 

85% RH so that 

1000 h equals 25 

years exposure 

(0C)

 

Years to 0.55% 

degradation (i.e. 

Hydrolysis Service 

Life) (y)

1000 Hours 

850C/85% RH 

Years equivalent 

(y)

PET is predicted to “fail” after 2064 h of 85 0C and 85% RH.
9

Site Specific Equivalent T and RH

R = A ∙ RRne −EE

k

RRwwwww w a a = RRWW =

∑ RRne −EE

k

∑ e −EE

k

1

n

This tells you what the relative humidity is at the temperatures where the most damage is done.

RRWW

ne − EE

k ee =

∑ RRne −EE

k

N

∴

∑ e −EE

k

N

= e − EE

k ee

The equivalent temperature (Teq) gives the temperature at RHWA for which constant 

conditions will produce a degradation rate equivalent to the yearly average. 

These terms cancel out

=

∑ RRne −EE

k

∑ e −EE

k

1

n

n

e − EE

k ee

∴ T = − K

EE ll ∑ e −EE

k

N
10

PET Hydrolysis Equivalent T and RH

Open 

Rack

Insulated 

Back

Open 

Rack

Insulated 

Back

Open 

Rack

Insulated 

Back

Open 

Rack

Insulated 

Back

Denver, Colorado 13,000 4,900 6,500 2,400 33 54 14 4.6

Munich, Germany 11,000 4,400 5,100 2,100 28 46 25 8.4

Albuquerque, New Mexico 9,000 3,200 4,400 1,500 37 58 13 4.2

Riyadh, Saudi Arabia 8,200 3,000 4,000 1,500 48 70 5.6 2.0

Phoenix, Arizona 3,400 1,300 1,700 630 46 68 9.8 3.3

Miami, Florida 1,100 510 530 250 37 54 36 14

Bangkok, Thailand 700 310 320 150 41 59 33 12

 

Years to 0.55% 

degradation (i.e. 

Hydrolysis Service 

Life) (y)

1000 Hours 

850C/85% RH 

Years equivalent 

(y)

Teq for Ea=129.3 

kJ/mol (0C)

RH, at Teq for 2nd 

order Kinetics of 

PET (%)

lll C

C−x

= A ∙ t ∙ RR2 ∙ e

−E

kk 
11

What Are Relevant Activation Energies

*R. R. Dixon, "Thermal Aging Predictions from an Arrhenus Plot with Only One Data Point," Electrical Insulation, IEEE Transactions on, vol. EI-15, pp. 331-334, 1980.

Degradation 

activation energy 

from Dixon*. Based 

on RTI testing for 

properties such as:

Elongation at Break

Flexural strength

Tensile Strength

Shear Strength

Burst Strength

Weight Loss

Dielectric Strength

Imp. Strength
12

For Diffusion Controlled Processes

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100 110

Counts

5 kJ/mol Activation Energy Bin

Diffusivity

Permeability

Solubility

Histogram for moisture ingress activation energy for PV polymeric materials.
13

Thermal Stress by Location and Mounting

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200

Equivalent Temperature (

°C)

Activation Energy (kJ/mol)

Equivalent Temperature

Riyadh

Bangkok

Denver

Munich

Dashed Lines:

Insulated Back

Solid Lines:

Rack Mounted
14

Modeling Moisture in the Front-EVA

Back-Sheet 

 

 Glass

H2O 

Back-EVA

PV Front-EVA 

Cell

The Back-EVA equilibrates with a characteristic time of about a day.

The Front-EVA equilibrates with halftimes of between a day and several years depending on 

the mounting configuration, location, and the position in front of the cell.

Uses the backside water concentration at the perimeter in a 2-D diffusion finite element 

algorithm. The cell size is 156+2 mm to account for water diffusing from the back to the front.
15

× 

Front Encapsulant Water Content

The front encapsulant traps in moisture seasonally making the center of the cell front the most

hydrolytically damaging area. 

The remainder of this presentation focuses on the center of the front side to evaluate the most

stressful position in the module. 

Rack mounted, Glass/Polymer modules

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0 1 2 3 4 5 6 7

Water Concentration (g/cm3)

Time (Years)

0

1.56

3.12

4.68

6.24

7.80

Distance

From

Cell Edge 

(cm)

Riyadh, Saudi Arabia

Munich, Germany

PV Cell

Profiles along this 

line are plotted.
16

RH Not Very Dependent Kinetics or Ea

0

10

20

30

40

50

60

0 25 50 75 100 125 150 175 200

Weighted RH (%)

Activation Energy (kJ/mol)

Bangkok, Thailand

1

2

3

4

5

n

Insulated Back

Rack Mounted
17

Small RH Dependence in All Climates

0

10

20

30

40

50

60

0 25 50 75 100 125 150 175 200

Weighted RH (%)

Activation Energy (kJ/mol and eV)

Solid Lines:

Rack Mounted

Dashed Lines:

Insulated Back

Darker Line:

n=2

Lighter Line:

n=1

Bangkok

Riyadh

Denver

Munich
18

85 0C/85% RH Equivalent Time-Bangkok 

0.1

1

10

100

1000

10000

100000

0 25 50 75 100 125 150 175 200

1000 h, 85 0C, 85% RH, 

Outdoor Equivalent (y)

Activation Energy (kJ/mol)

Bangkok, Thailand

 Rack, n=2

 Rack, n=1

 Rack, n=0

 Insulated, n=2

 Insulated, n=1

 Insulated, n=0

Solid Lines: 

Rack Mounted

Dashed Lines: 

Insulated Back

25

85% RH
19

85 0C/85% RH Equivalent Time-Riyadh 

The unknown humidity dependence results in a 1000× uncertainty in the acceleration

0.1

1

10

100

1000

10000

100000

0 25 50 75 100 125 150 175 200

1000 h, 85 0C, 85% RH, 

Outdoor Equivalent (y)

Activation Energy (kJ/mol)

Riyadh, Saudi Arabia

 Rack, n=2

 Rack, n=1

 Rack, n=0

 Insulated, n=2

 Insulated, n=1

 Insulated, n=0

Solid Lines: 

Rack Mounted

Dashed Lines: 

Insulated Back

25

85% RH
20

Good RH Choice Reduces Uncertainty

0.1

1

10

100

1000

10000

100000

0 25 50 75 100 125 150 175 200

1000 h, 85 0C, 5% RH, 

Outdoor Equivalent (y)

Activation Energy (kJ/mol)

Riyadh, Saudi Arabia

 Rack, n=2

 Rack, n=1

 Rack, n=0

 Insulated, n=2

 Insulated, n=1

 Insulated, n=0

Solid Lines: 

Rack Mounted

Dashed Lines: 

Insulated Back

25

5% RH

Testing using a chamber humidity of 5% vs. 85% significantly reduces the variability in the 

acceleration factor.
21

The Highest RH You Might Want is ~25%

0.1

1

10

100

1000

10000

100000

0 25 50 75 100 125 150 175 200

1000 h, 85 0C, 25% RH, 

Outdoor Equivalent (y)

Activation Energy (kJ/mol)

Bangkok, Thailand

 Rack, n=2

 Rack, n=1

 Rack, n=0

 Insulated, n=2

 Insulated, n=1

 Insulated, n=0

Solid Lines: 

Rack Mounted

Dashed Lines: 

Insulated Back

25

25% RH
22

Damp Heat vs. Low RH Stress Test

Without knowing the moisture induced degradation kinetics, it is better to use a low RH and 

accelerate processes principally by thermal acceleration.

0.1

1

10

100

1000

10000

100000

0 25 50 75 100 125 150 175 200

1000 h, 85 0C, 85% RH, 

Outdoor Equivalent (y)

Activation Energy (kJ/mol)

Riyadh, Saudi Arabia

 Rack, n=2

 Rack, n=1

 Rack, n=0

 Insulated, n=2

 Insulated, n=1

 Insulated, n=0

Solid Lines: 

Rack Mounted

Dashed Lines: 

Insulated Back

25

85% RH

0.1

1

10

100

1000

10000

100000

0 25 50 75 100 125 150 175 200

1000 h, 85 0C, 85% RH, 

Outdoor Equivalent (y)

Activation Energy (kJ/mol)

Bangkok, Thailand

 Rack, n=2

 Rack, n=1

 Rack, n=0

 Insulated, n=2

 Insulated, n=1

 Insulated, n=0

Solid Lines: 

Rack Mounted

Dashed Lines: 

Insulated Back

25

85% RH

0.1

1

10

100

1000

10000

100000

0 25 50 75 100 125 150 175 200

1000 h, 85 0C, 25% RH, 

Outdoor Equivalent (y)

Activation Energy (kJ/mol)

Bangkok, Thailand

 Rack, n=2

 Rack, n=1

 Rack, n=0

 Insulated, n=2

 Insulated, n=1

 Insulated, n=0

Solid Lines: 

Rack Mounted

Dashed Lines: 

Insulated Back

25

25% RH

0.1

1

10

100

1000

10000

100000

0 25 50 75 100 125 150 175 200

1000 h, 85 0C, 5% RH, 

Outdoor Equivalent (y)

Activation Energy (kJ/mol)

Riyadh, Saudi Arabia

 Rack, n=2

 Rack, n=1

 Rack, n=0

 Insulated, n=2

 Insulated, n=1

 Insulated, n=0

Solid Lines: 

Rack Mounted

Dashed Lines: 

Insulated Back

25

5% RH
23

Conclusions

• With respect to PET hydrolysis, 85 0C/85% RH, 

may be equivalent to hundreds or thousands of 

years.

• For thermal and/or moisture induced failure, the 

mounting configuration can be as important as 

the location.

• Care must be taken in accelerated stress testing 

to account for the variable relative acceleration 

of the different degradation modes.

• Choosing the right humidity level for accelerated 

stress testing can dramatically decrease the 

uncertainty in the results.
24

Acknowledgements 

Sarah Kurtz

John Wohlgemuth

David Miller

Peter Hacke

This work was supported by the U.S. 

Department of Energy under Contract No. 

DE-AC36-08-GO28308 with the National 

Renewable Energy Laboratory.